Geometry

Question Analysis  

Determine the -coordinate of a point on the unit circle in Quadrant I, using the Pythagorean theorem and properties of 45-45-90 triangles.  

 

Key Concept Explanation  

Unit Circle Equation: . For , this becomes (since ).  

This reflects a 45-45-90 triangle where legs are equal, and hypotenuse = 1 (unit circle radius).  

 

Step-by-Step Solution  

1. Substitute into the unit circle equation:  

2. Solve for in Quadrant I (where x > 0):  

 

Option Analysis  

: Correct (satisfies and )